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Full text of "Text Book Of Mechanical Engineering"

490

Curves of Velocity.

taneous motion, in direction only, of the two ends P and W of a
link, each poiat may be supposed, for the instant, to be travelling
in a separate circle, whose radius will be at right angles to the
aforesaid motion, and the two radii will,, unless the directions of
motion are parallel, meet on one side or other of the line P "W.
The meeting point is known as the instantaneous or virtual
"centre, and the ratio of the velocities of P and W will be the
same as that of the radii Jrom the virtual centre. Of course these
may change at every instant, and the centre itself will move along
a path known as the centrode.

Crank and Connecting Rod (Fig. 452).—In'the position
given, W is travelling tangentially, and w D is its virtual radius,
while P is moving towards A, and has a radius P D. D then is the
virtual centre, and at the instant considered, the movements being
along the dotted arcs, pl iv^

vel. P __ D P
vel. W ~" DW

Taking various other positions, we may obtain a series of
virtual centres; and through them draw the centrode E D F, where
E and M are the positions of P when W crosses the line K. E. The
curve passes out to infinity at F and o, reappearing at L and Q, the
direction heing given by the line JP when W is at G and P at H.
This means that P and W have then equal velocities. The
relative velocities being found for any position, their inversion will
give the relation of the forces P and W.

Curve of Velocities.—It is often required to construct a
curve of velocities for one of the points, when the other mows
uniformly. Taking the second diagram in Fig, 452, the triangles
w c A. and w P D are similar, so that

vel. P _ JDJ> _ A c
vel W """* D w "" A w

Assuming "W to rnove uniformly, being provided with a fly-
wheel, A w will represent crank velocity^ while the projection of
P W upon the vertical at c or £ will give AC or &c the piston
velocity, In Fig. 453 the value AC is found and transferred to
the line A w at A E, and this being done for all positions, the ovals
or polar curve may be traced, whose rwttus meter always shews Ps